Problem: Simplify the following expression: $\sqrt{176}+\sqrt{275}-\sqrt{11}$
Explanation: First, try to factor any perfect squares out of the radicals. $= \sqrt{176}+\sqrt{275}-\sqrt{11}$ $= \sqrt{16 \cdot 11}+\sqrt{25 \cdot 11}-\sqrt{11}$ Separate the radicals and simplify. $= \sqrt{16} \cdot \sqrt{11}+\sqrt{25} \cdot \sqrt{11}-\sqrt{11}$ $= 4\sqrt{11}+5\sqrt{11}-\sqrt{11}$ Finally, simplify by combining the terms. $= ( 4 + 5 - 1 )\sqrt{11} = 8\sqrt{11}$